Question

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If the measures of ∠P, ∠Q, ∠R, and ∠S of a quadrilateral PQRS are in the ratio 2 : 4 : 5 : 7, then what are the respective measures of ∠P, ∠Q, ∠R, and ∠S?​

Answer 1

Given :-

If the measures of ∠P, ∠Q, ∠R, and ∠S of a quadrilateral PQRS are in the ratio 2 : 4 : 5 : 7,

To Find :-

what are the respective measures of ∠P, ∠Q, ∠R, and ∠S?​

Solution :-

Let the angles be 2x, 4x, 5x and 7x

2x + 4x + 5x + 7x = 360

18x = 360

x = 360/18

x = 20

Therefore

∠P = 2(20) = 40

∠Q = 4(20) = 80

∠R = 5(20) = 100

∠S = 7(20) = 140

Answer 2

➠GIVEN :

• the measures of angle are in the ratio 2:4:5:7 in quadrilateral PQRS

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➠TO FIND :

• measurements of all angles of PQRS.

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➠METHOD :

let angles of quadrilateral be 2x, 4x, 5x and 7x respectively

↪️2x + 4x + 5x + 7x = 360° [by angle sum property of a quadrilateral ]

↪2x + 4x + 5x + 7x = 360°

↪18x = 360°

↪x = 20°

hence,

∠P = ( 2 × X) = 2 × 20° = 40°

∠Q = ( 4 × X) = 4 × 20° = 80°

∠R = ( 5 × X) = 5 × 20° = 100°

∠S = ( 7 × X) = 7 × 20° = 140°

hope it helps..

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